The octonionic Fourier transform: Uncertainty relations and convolution

被引：17

作者：

Lian, Pan ^{[1
]}

机构：

[1] Tianjin Normal Univ, Sch Math Sci, Binshui West Rd 393, Tianjin 300387, Peoples R China

来源：

SIGNAL PROCESSING | 2019年 / 164卷

关键词：

Octonion; Fourier transform; Quaternion; Uncertainty principle; Convolution; PRINCIPLE;

D O I：

10.1016/j.sigpro.2019.06.015

中图分类号：

TM [电工技术]; TN [电子技术、通信技术];

学科分类号：

0808 ; 0809 ;

摘要：

The uncertainty principle is a fundamental principle in mathematics and physics, and also plays an important role in signal processing. On the other side, the octonion Fourier transform has got a lot of attentions in recent years. It is the aim of this paper to establish various uncertainty relations for this new hyper-complex Fourier transform. Based on the relations between the octonion Fourier transform and the quaternion Fourier transform, several uncertainty inequalities are derived neatly, including the logarithmic uncertainty inequality, local uncertainty inequalities, generalized global uncertainty inequality and the Benedicks-Amrein-Berthier inequality. In addition, the Mustard convolution associated to the octonion Fourier transform is discussed as well. (C) 2019 Elsevier B.V. All rights reserved.

引用

页码：295 / 300

页数：6

共 50 条

[21] A General Geometric Fourier Transform Convolution Theorem
Bujack, Roxana
Scheuermann, Gerik
Hitzer, Eckhard
ADVANCES IN APPLIED CLIFFORD ALGEBRAS, 2013, 23 (01) : 15 - 38
[22] CONVOLUTION, PRODUCT AND FOURIER-TRANSFORM OF DISTRIBUTIONS
KAMINSKI, A
STUDIA MATHEMATICA, 1982, 74 (01) : 83 - 96
[23] CONVOLUTION AND FOURIER-TRANSFORM OF HIDA DISTRIBUTIONS
KUO, HH
LECTURE NOTES IN CONTROL AND INFORMATION SCIENCES, 1992, 176 : 165 - 176
[24] Chrestenson Transform and its Relations with Fourier Transform
Zhou, Mingyong
Shi, Xiaole
Liu, Zhongkan
2015 THIRD INTERNATIONAL CONFERENCE ON ROBOT, VISION AND SIGNAL PROCESSING (RVSP), 2015, : 212 - 215
[25] Product and convolution theorems for the fractional Fourier transform
Almeida, LB
IEEE SIGNAL PROCESSING LETTERS, 1997, 4 (01) : 15 - 17
[26] An uncertainty principle for quaternion Fourier transform
Bahri, Mawardi
Hitzer, Eckhard S. M.
Hayashi, Akihisa
Ashino, Ryuichi
COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2008, 56 (09) : 2398 - 2410
[27] Uncertainty Principles for the Clifford–Fourier Transform
Jamel El Kamel
Rim Jday
Advances in Applied Clifford Algebras, 2017, 27 : 2429 - 2443
[28] Uncertainty principle for the quaternion Fourier transform
Lian, Pan
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2018, 467 (02) : 1258 - 1269
[29] The uncertainty principle for the octonion Fourier transform
Zayed, Mohra
El Haoui, Youssef
MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2023, 46 (02) : 2651 - 2666
[30] Uncertainty relation for the discrete fourier transform
Massar, Serge
Spindel, Philippe
PHYSICAL REVIEW LETTERS, 2008, 100 (19)

← 1 2 3 4 5 →